Question

A Cartesian coordinate system with the x-axis ranging from negative 10 to 10 and the y-axis ranging from negative 7 to 10. There are two triangles plotted, a triangle LMN with vertices labeled as L(1, 1), M(7, 2), and N(5, 7) A triangle L double prime M double prime N double prime with vertices labeled as L double prime (2, negative 1), M double prime (negative 4, 0), and N double prime (negative 2, 5).


Image Long DescriptionThe triangle upper L upper M upper N passes through upper L left parenthesis 1 comma 1 right parenthesis, upper M left parenthesis 7 comma 2 right parenthesis, and upper N left parenthesis 5 comma 7 right parenthesis. The triangle upper L double prime upper M double prime upper N double prime passes through upper L double prime left parenthesis 2 comma negative 1 right parenthesis, upper M double prime left parenthesis negative 4 comma 0 right parenthesis, and upper N double prime left parenthesis negative 2 comma 5 right parenthesis.What composition transformation rule has △LMN
△
𝐿
𝑀
𝑁
, L(1,1)
𝐿
(
1
,
1
)
, M(7,2)
𝑀
(
7
,
2
)
, and N(5,7)
𝑁
(
5
,
7
)
map onto △L"M"N"
△
𝐿
"
𝑀
"
𝑁
"
, L"(2,−1)
𝐿
"
(
2
,
−
1
)
, M"(−4,0)
𝑀
"
(
−
4
,
0
)
, and N"(−2,5)
𝑁
"
(
−
2
,
5
)
?

(1 point)
Responses

a rotation of 270 degrees clockwise and a move right by 3 and up by 2
a rotation of 270 degrees clockwise and a move right by 3 and up by 2

a reflection across the y-axis and a move to the right by 3 and down by 2
a reflection across the y -axis and a move to the right by 3 and down by 2

a reflection across the x-axis and a move to the left by 3 and down by 2
a reflection across the x -axis and a move to the left by 3 and down by 2

a reflection across the y-axis and a move to the left by 5 and up by 3

Answer 1

Reflection across the y-axis, then translation right 3 and down 2.

In coordinates: (x,y) -> (-x, y) -> (-x+3, y-2), so overall (x,y) -> (-x+3, y-2).

Check:
- L(1,1) -> (-1,1) -> (2,-1) = L''
- M(7,2) -> (-7,2) -> (-4,0) = M''
- N(5,7) -> (-5,7) -> (-2,5) = N''